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Boolean logic

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(mathematics, logic, computing) A system of symbolic logic that is the basis of Boolean algebra

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system of symbolic logic
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Just like Fuzzy logic is an extension of Boolean logic (which uses absolute truth and falsehood only, and nothing in between), fuzzy numbers are an extension of real numbers.
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For example, Boolean logic uses this condensed truth table notation: This notation is useful especially if the operations are commutative, although one can additionally specify that the rows are the first operand and the columns are the second operand.
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In boolean logic, a disjunctive normal form (DNF) is a standardization (or normalization) of a logical formula which is a disjunction of conjunctive clauses; it can also be described as an OR of ANDs, a sum of products, or (in philosophical logic) a cluster concept.
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In Boolean algebra, circuit minimization is the problem of obtaining the smallest logic circuit (Boolean formula) that represents a given Boolean function or truth table.
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The ACM Computing Classification System in particular regards: Section F.3 on Logics and meanings of programs and F.4 on Mathematical logic and formal languages as part of the theory of computer science: this work covers formal semantics of programming languages, as well as work of formal methods such as Hoare logic; Boolean logic as fundamental to computer hardware: particularly, the system's section B.2 on Arithmetic and logic structures, relating to operatives AND, NOT, and OR; Many fundamental logical formalisms are essential to section I.2 on artificial intelligence, for example modal logic and default logic in Knowledge representation formalisms and methods, Horn clauses in logic programming, and description logic.
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A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001).
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In digital electronics and computer science (fields of applied logic engineering and mathematics), truth tables can be used to reduce basic boolean operations to simple correlations of inputs to outputs, without the use of logic gates or code.
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Boolean functions are often represented by sentences in propositional logic, and sometimes as multivariate polynomials over GF(2), but more efficient representations are binary decision diagrams (BDD), negation normal forms, and propositional directed acyclic graphs (PDAG).
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In the case where k = 0, the "function" is essentially a constant element of B. Every k-ary Boolean function can be expressed as a propositional formula in k variables x1, ..., xk, and two propositional formulas are logically equivalent if and only if they express the same Boolean function.
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Many classes of algebras over a field or over a ring have a specific name: Associative algebra Non-associative algebra Lie algebra Hopf algebra C*-algebra Symmetric algebra Exterior algebra Tensor algebra In measure theory, Sigma-algebra Algebra over a set In category theory F-algebra and F-coalgebra T-algebra In logic, Relation algebra, a residuated Boolean algebra expanded with an involution called converse.
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A waveform that switches representing the two states of a Boolean value (0 and 1, or low and high, or false and true) is referred to as a digital signal or logic signal or binary signal when it is interpreted in terms of only two possible digits.
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11 sinne gevind in 4 ms. Hulle kom uit baie bronne en word nie nagegaan nie.